A149049 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 10, 39, 145, 630, 2593, 11591, 50017, 229816, 1027680, 4787417, 21844486, 103089050, 478192777, 2274130170, 10665707770, 51086135767, 241825054742, 1163848294068, 5546693978070, 26813667994663, 128532843066514, 623362741860976, 3001574315408743, 14600655776691757, 70579346335119111

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A327847 A111749 A149048 * A149050 A300974 A149051

Adjacent sequences: A149046 A149047 A149048 * A149050 A149051 A149052

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved